18 citations · 78 across the 36 of their papers we have counts for
5 papers · 1 filter
The gamma - Borel conjecture
Arnold W. Miller
In this paper we show that it is relatively consistent with ZFC that every gamma-set is countable while not every strong measure zero set is countable. This answers a question of P…
Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set
Maxim R. Burke, Arnold W. Miller
We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor set C such that A intersect C is…
Ultrafilters with property (s)
Arnold W. Miller
A set X which is a subset of the Cantor set has property (s) (Marczewski (Spzilrajn)) iff for every perfect set P there exists a perfect set Q contained in P such that Q is a subse…
On relatively analytic and Borel subsets
Arnold W. Miller
Define z to be the smallest cardinality of a function f:X->Y with X and Y sets of reals such that there is no Borel function g extending f. In this paper we prove that it is relati…
A nonhereditary Borel-cover gamma-set
Arnold W. Miller
In this paper we prove that if there is a Borel-cover gamma-set of cardinality the continuum, then there is one which is not hereditary. A set of reals X is a Borel-cover gamma-set…